Geodesic
Homogenization of elliptic operators with periodic coefficients depending on the spectral parameter
Algebra i analiz, Tome 27 (2015) no. 4, pp. 87-166.

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     url = {http://geodesic.mathdoc.fr/item/AA_2015_27_4_a6/}
}
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T. A. Suslina. Homogenization of elliptic operators with periodic coefficients depending on the spectral parameter. Algebra i analiz, Tome 27 (2015) no. 4, pp. 87-166. http://geodesic.mathdoc.fr/item/AA_2015_27_4_a6/

[1] Bakhvalov N. S., Panasenko G. P., Osrednenie protsessov v periodicheskikh sredakh, Nauka, M., 1984 | MR

[2] Bensoussan A., Lions J.-L., Papanicolaou G., Asymptotic analysis for periodic structures, Stud. Math. Appl., 5, North-Holland Publ. Co., Amsterdam–New York, 1978 | MR | Zbl

[3] Birman M., Suslina T., “Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics”, Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), Oper. Theory Adv. Appl., 129, Birkhäuser, Basel, 2001, 71–107 | MR | Zbl

[4] Birman M. Sh., Suslina T. A., “Periodicheskie differentsialnye operatory vtorogo poryadka. Porogovye svoistva i usredneniya”, Algebra i analiz, 15:5 (2003), 1–108 | MR | Zbl

[5] Birman M. Sh., Suslina T. A., “Usrednenie periodicheskikh ellipticheskikh differentsialnykh operatorov s uchetom korrektora”, Algebra i analiz, 17:6 (2005), 1–104 | MR | Zbl

[6] Birman M. Sh., Suslina T. A., “Usrednenie periodicheskikh differentsialnykh operatorov s uchetom korrektora. Priblizhenie reshenii v klasse Soboleva $H^1(\mathbb R^d)$”, Algebra i analiz, 18:6 (2006), 1–130 | MR | Zbl

[7] Griso G., “Error estimate and unfolding for periodic homogenization”, Asymptot. Anal., 40:3–4 (2004), 269–286 | MR | Zbl

[8] Griso G., “Interior error estimate for periodic homogenization”, Anal. Appl., 4:1 (2006), 61–79 | DOI | MR | Zbl

[9] Zhikov V. V., “Ob operatornykh otsenkakh v teorii usredneniya”, Dokl. RAN, 403:3 (2005), 305–308 | MR | Zbl

[10] Zhikov V. V., “O nekotorykh otsenkakh iz teorii usredneniya”, Dokl. RAN, 406:5 (2006), 597–601 | MR | Zbl

[11] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Nauka, M., 1993 | MR

[12] Zhikov V. V., Pastukhova S. E., “On operator estimates for some problems in homogenization theory”, Russ. J. Math. Phys., 12:4 (2005), 515–524 | MR | Zbl

[13] Kenig C. E., Lin F., Shen Z., “Convergence rates in $L^2$ for elliptic homogenization problems”, Arch. Ration. Mech. Anal., 203:3 (2012), 1009–1036 | DOI | MR | Zbl

[14] Kondratev V. A., Eidelman S. D., “Ob usloviyakh na granichnuyu poverkhnost v teorii ellipticheskikh granichnykh zadach”, Dokl. AN SSSR, 246:4 (1979), 812–815 | MR | Zbl

[15] Mazya V. G., Shaposhnikova T. O., Multiplikatory v prostranstvakh differentsiruemykh funktsii, LGU, Leningrad, 1986 | MR

[16] McLean W., Strongly elliptic systems and boundary integral equations, Cambridge Univ. Press, Cambridge, 2000 | MR | Zbl

[17] Meshkova Yu. M., Suslina T. A., “Usrednenie reshenii nachalno-kraevykh zadach dlya parabolicheskikh sistem”, Funkts. anal. i ego pril., 49:1 (2015), 88–93 | DOI | Zbl

[18] Meshkova Y. M., Suslina T. A., “Homogenization of initial boundary value problems for parabolic systems with periodic coefficients”, Appl. Anal. (to appear)

[19] Necas J., Direct methods in the theory of elliptic equations, Springer Monogr. Math., Springer-Verlag, Heidelberg, 2012 | DOI | MR | Zbl

[20] Pakhnin M. A., Suslina T. A., “Usrednenie ellipticheskoi zadachi Dirikhle: otsenki pogreshnosti v $(L_2\to H^1)$-norme”, Funkts. anal. i ego pril., 46:2 (2012), 92–96 | DOI | MR | Zbl

[21] Pakhnin M. A., Suslina T. A., “Operatornye otsenki pogreshnosti pri usrednenii ellipticheskoi zadachi Dirikhle v ogranichennoi oblasti”, Algebra i analiz, 24:6 (2012), 139–177 | MR | Zbl

[22] Stein I. M., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[23] Suslina T. A., “Operatornye otsenki pogreshnosti v $L_2$ pri usrednenii ellipticheskoi zadachi Dirikhle”, Funkts. anal. i ego pril., 46:3 (2012), 91–96 | DOI | MR | Zbl

[24] Suslina T. A., “Homogenization of the Dirichlet problem for elliptic systems: $L_2$-operator error estimates”, Mathematika, 59:2 (2013), 463–476 | DOI | MR | Zbl

[25] Suslina T. A., “Homogenization of the Neumann problem for elliptic systems with periodic coefficients”, SIAM J. Math. Anal., 45:6 (2013), 3453–3493 | DOI | MR | Zbl

[26] Suslina T. A., “Usrednenie ellipticheskikh zadach v zavisimosti ot spektralnogo parametra”, Funkts. anal. i ego pril., 48:4 (2014), 88–94 | DOI | Zbl